Question
Factor polynomial x^4-3x^3+2x^2
Answers
GPT 3.5
To factor the polynomial x^4 - 3x^3 + 2x^2, we can first factor out the greatest common factor, which is x^2:
x^4 - 3x^3 + 2x^2 = x^2(x^2 - 3x + 2)
Now, we need to factor the quadratic expression x^2 - 3x + 2. To factor this, we can look for two numbers whose product is 2 and whose sum is -3. The numbers -1 and -2 satisfy these conditions, so we can rewrite the expression as:
x^2 - 3x + 2 = x^2 - 2x - x + 2
= x(x - 2) - 1(x - 2)
= (x - 1)(x - 2)
Therefore, the factored form of the polynomial x^4 - 3x^3 + 2x^2 is x^2(x - 1)(x - 2).
x^4 - 3x^3 + 2x^2 = x^2(x^2 - 3x + 2)
Now, we need to factor the quadratic expression x^2 - 3x + 2. To factor this, we can look for two numbers whose product is 2 and whose sum is -3. The numbers -1 and -2 satisfy these conditions, so we can rewrite the expression as:
x^2 - 3x + 2 = x^2 - 2x - x + 2
= x(x - 2) - 1(x - 2)
= (x - 1)(x - 2)
Therefore, the factored form of the polynomial x^4 - 3x^3 + 2x^2 is x^2(x - 1)(x - 2).